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A327414 Minimal prime partition representation of even integers. 1
0, 2, 6, 20, 56, 120, 792, 364, 560, 8568, 1140, 1540, 42504, 2600, 98280, 2035800, 4960, 5984, 376992, 12620256, 9880, 850668, 13244, 15180, 1712304, 19600, 2598960, 177100560, 27720, 4582116, 386206920, 37820, 41664, 8936928, 969443904, 54740, 13991544 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A partition is prime if all parts are primes. A partition of an even integer n > 2 is minimal if it has at most two parts, one of which is the greatest prime less than n - 1. The terms of the sequence are the multinomials of these partition. By convention a(0) = 0 and a(1) = 2.

LINKS

Table of n, a(n) for n=0..36.

Eric Weisstein's World of Mathematics, Prime Partition

FORMULA

For n >= 2 let a(n) be the multinomial of P where P is the partition [p, 2n - p] with p the greatest prime less than 2n - 1.

EXAMPLE

n   2n  partition a(n)

2   4 :  [2,  2]   6

3   6 :  [3,  3]   20

4   8 :  [5,  3]   56

5   10:  [7,  3]   120

6   12:  [7,  5]   792

7   14:  [11, 3]   364

8   16:  [13, 3]   560

9   18:  [13, 5]   8568

10  20:  [17, 3]   1140

11  22:  [19, 3]   1540

12  24:  [19, 5]   42504

13  26:  [23, 3]   2600

14  28:  [23, 5]   98280

15  30:  [23, 7]   2035800

PROG

(SageMath)

def a(n):

    if n < 2: return 2*n

    p = previous_prime(2*n - 1)

    return multinomial([p, 2*n - p])

print([a(n) for n in range(40)])

CROSSREFS

Cf. A327413.

Sequence in context: A045655 A303307 A321192 * A110295 A027294 A231538

Adjacent sequences:  A327411 A327412 A327413 * A327415 A327416 A327417

KEYWORD

nonn

AUTHOR

Peter Luschny, Sep 07 2019

STATUS

approved

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Last modified March 5 11:27 EST 2021. Contains 341823 sequences. (Running on oeis4.)